Deterministic sub-linear space LCE data structures with efficient construction

Given a string $S$ of $n$ symbols, a longest common extension query $\mathsf{LCE}(i,j)$ asks for the length of the longest common prefix of the $i$th and $j$th suffixes of $S$. LCE queries have several important applications in string processing, perhaps most notably to suffix sorting. Recently, Bille et al. (J. Discrete Algorithms 25:42-50, 2014, Proc. CPM 2015: 65-76) described several data structures for answering LCE queries that offers a space-time trade-off between data structure size and query time. In particular, for a parameter $1 \leq \tau \leq n$, their best deterministic solution is a data structure of size $O(n/\tau)$ which allows LCE queries to be answered in $O(\tau)$ time. However, the construction time for all deterministic versions of their data structure is quadratic in $n$. In this paper, we propose a deterministic solution that achieves a similar space-time trade-off of $O(\tau\min\{\log\tau,\log\frac{n}{\tau}\})$ query time using $O(n/\tau)$ space, but significantly improve the construction time to $O(n\tau)$.Comment: updated titl

Dynamics of a tracer granular particle as a non-equilibrium Markov process

The dynamics of a tracer particle in a stationary driven granular gas is investigated. We show how to transform the linear Boltzmann equation describing the dynamics of the tracer into a master equation for a continuous Markov process. The transition rates depend upon the stationary velocity distribution of the gas. When the gas has a Gaussian velocity probability distribution function (pdf), the stationary velocity pdf of the tracer is Gaussian with a lower temperature and satisfies detailed balance for any value of the restitution coefficient $\alpha$. As soon as the velocity pdf of the gas departs from the Gaussian form, detailed balance is violated. This non-equilibrium state can be characterized in terms of a Lebowitz-Spohn action functional $W(\tau)$ defined over trajectories of time duration $\tau$. We discuss the properties of this functional and of a similar functional $\bar{W}(\tau)$ which differs from the first for a term which is non-extensive in time. On the one hand we show that in numerical experiments, i.e. at finite times $\tau$, the two functionals have different fluctuations and $\bar{W}$ always satisfies an Evans-Searles-like symmetry. On the other hand we cannot observe the verification of the Lebowitz-Spohn-Gallavotti-Cohen (LS-GC) relation, which is expected for $W(\tau)$ at very large times $\tau$. We give an argument for the possible failure of the LS-GC relation in this situation. We also suggest practical recipes for measuring $W(\tau)$ and $\bar{W}(\tau)$ in experiments.Comment: 16 pages, 3 figures, submitted for publicatio

Fluctuation-Dissipation relations in Driven Granular Gases

We study the dynamics of a 2d driven inelastic gas, by means of Direct Simulation Monte Carlo (DSMC) techniques, i.e. under the assumption of Molecular Chaos. Under the effect of a uniform stochastic driving in the form of a white noise plus a friction term, the gas is kept in a non-equilibrium Steady State characterized by fractal density correlations and non-Gaussian distributions of velocities; the mean squared velocity, that is the so-called {\em granular temperature}, is lower than the bath temperature. We observe that a modified form of the Kubo relation, which relates the autocorrelation and the linear response for the dynamics of a system {\em at equilibrium}, still holds for the off-equilibrium, though stationary, dynamics of the systems under investigation. Interestingly, the only needed modification to the equilibrium Kubo relation is the replacement of the equilibrium temperature with an effective temperature, which results equal to the global granular temperature. We present two independent numerical experiment, i.e. two different observables are studied: (a) the staggered density current, whose response to an impulsive shear is proportional to its autocorrelation in the unperturbed system and (b) the response of a tracer to a small constant force, switched on at time $t_w$, which is proportional to the mean-square displacement in the unperturbed system. Both measures confirm the validity of Kubo's formula, provided that the granular temperature is used as the proportionality factor between response and autocorrelation, at least for not too large inelasticities.Comment: 11 pages, 7 figures, submitted for publicatio

Rapid and Accurate Identification of Nontuberculous Mycobacteria Directly from Positive Primary MGIT Cultures by MALDI-TOF MS

Over the last years, nontuberculous mycobacteria (NTM) have emerged as important human pathogens. Accurate and rapid mycobacterial species identification is needed to successfully diagnose, treat, and manage infections caused by NTM. Matrix-assisted laser desorption ionization time-of-flight mass spectrometry, MALDI-TOF MS, was demonstrated to effectively identify mycobacteria isolates subcultured from solid or liquid media rather than new positive cultures. The present study aims to develop a new extraction protocol to yield rapid and accurate identification of NTM from primary MGIT cultures by MALDI-TOF MS. A total of 60 positive MGIT broths were examined by the Bruker Biotyper system with Mycobacteria Library v. 2.0 (Bruker Daltonics GmbH & Co. KG., Bremen, Germany). The results were compared with those obtained by the molecular method, line probe assay GenoType Mycobacterium CM/AS/NTM-DR. All samples were concordantly identified by MALDI-TOF MS and the molecular test for all the tested mycobacteria. Fifty-seven (95%) MGIT positive cultures for NTM from clinical samples had a MALDI-TOF MS analysis score S ≥ 1.8. Although a small number of strains and a limited diversity of mycobacterial species were analysed, our results suggest that MALDI-TOF MS could represent a promising routine diagnostic tool for identifying mycobacterial species directly from primary liquid culture

Sand stirred by chaotic advection

We study the spatial structure of a granular material, N particles subject to inelastic mutual collisions, when it is stirred by a bidimensional smooth chaotic flow. A simple dynamical model is introduced where four different time scales are explicitly considered: i) the Stokes time, accounting for the inertia of the particles, ii) the mean collision time among the grains, iii) the typical time scale of the flow, and iv) the inverse of the Lyapunov exponent of the chaotic flow, which gives a typical time for the separation of two initially close parcels of fluid. Depending on the relative values of these different times a complex scenario appears for the long-time steady spatial distribution of particles, where clusters of particles may or not appear.Comment: 4 pages, 3 figure

Attempted density blowup in a freely cooling dilute granular gas: hydrodynamics versus molecular dynamics

It has been recently shown (Fouxon et al. 2007) that, in the framework of ideal granular hydrodynamics (IGHD), an initially smooth hydrodynamic flow of a granular gas can produce an infinite gas density in a finite time. Exact solutions that exhibit this property have been derived. Close to the singularity, the granular gas pressure is finite and almost constant. This work reports molecular dynamics (MD) simulations of a freely cooling gas of nearly elastically colliding hard disks, aimed at identifying the "attempted" density blowup regime. The initial conditions of the simulated flow mimic those of one particular solution of the IGHD equations that exhibits the density blowup. We measure the hydrodynamic fields in the MD simulations and compare them with predictions from the ideal theory. We find a remarkable quantitative agreement between the two over an extended time interval, proving the existence of the attempted blowup regime. As the attempted singularity is approached, the hydrodynamic fields, as observed in the MD simulations, deviate from the predictions of the ideal solution. To investigate the mechanism of breakdown of the ideal theory near the singularity, we extend the hydrodynamic theory by accounting separately for the gradient-dependent transport and for finite density corrections.Comment: 11 pages, 9 figures, accepted for publication on Physical Review

Vaccination for seasonal influenza in patients with cancer: Recommendations of the Italian Society of Medical Oncology (AIOM)

Background: Influenza virus causes annual epidemics in the winter\u2013spring season with significant morbidity in the general population and important mortality in high-risk groups, including cancer patients. Opinions on the suitability of patients with malignancies not undergoing active treatment and in different phases of antineoplastic therapy, to receive influenza vaccination, vary considerably among oncologists, sometimes even within one center. Methods: We reviewed available data, including recommendations by national health authorities, on impact of influenza in patients with cancer and their capacity to mount protective immunological responses to vaccination, thus allowing, on behalf of Italian Association of Medical Oncology, to make suitable recommendations for the prevention and treatment of seasonal influenza. Results and discussion: Patients with cancer often have disease- or treatment-related immunosuppression, and as a consequence, they may have a suboptimal serologic response to influenza vaccination. The protective effect of the differ- ent preparations of influenza vaccines in patients with cancer has not been widely investigated, especially in adult patients harboring solid tumors. The optimal timing for administration of influenza vaccines in patients receiving chemotherapy is also not clearly defined. However, since vaccination is the most effective method, along with antiviral drugs in selected patients, for preventing influenza infection, it has to be recommended for cancer patients. Implementing vaccination of close contacts of oncology patients would be an additional tool for enhancing protection in fragile patient populations